num genre
1 125 Horror
2 110 Thrillers
3 38 Comedies
4 19 SciFi&Fantasy
5 12 Cult
6 2 Documentaties
7 2 Romantic
December 9, 2024
CI <- function(data, coverage_prob){
#Generates a normal prediction interval with an intended coverage probability of coverage_prob based on a vector of numeric data
lower_zscore <- qnorm((1-coverage_prob)/2)
upper_zscore <- qnorm(((1-coverage_prob)/2) + coverage_prob)
avg <- mean(data)
stan_d <- sd(data)
lower_bound <- avg + lower_zscore*stan_d
upper_bound <- avg + upper_zscore*stan_d
return(data.frame(PI_percentage = coverage_prob, lower = lower_bound, upper = upper_bound))
}one_beta_simulation <- function(n, alpha, beta, ci_prop){
#Assesses prediction accuracy and actual coverage probability of a normal prediction interval when used on a vector of numeric data of size n. The numeric data is generated from a beta distribution with parameters alpha and beta.
cover_df <- CI(rbeta(n, alpha, beta), ci_prop)
cover_prop <- pbeta(cover_df[1, "upper"], alpha, beta) - pbeta(cover_df[1, "lower"], alpha, beta)
mean_in_interval <- .5 >= cover_df[1, "lower"] & .5 <= cover_df[1,"upper"]
param_df <- data.frame(cover = cover_prop, alpha = rep(alpha, nrow(cover_df)), beta = rep(beta, nrow(cover_df)), mean_in_interval = mean_in_interval)
df <- cbind(cover_df, param_df)
return(df)
}beta_sims_n <- function(n){
#Iterates over a vector of possible alpha = beta values and applies one_beta_simulation to each possible value of alpha/beta. All simulations use data of sample size n.
df1 <- map(parameters,\(param) one_beta_simulation(n, param, param, ci) ) %>%
list_rbind()
df2 <- data.frame(n = rep(n, nrow(df1)))
df <- cbind(df2, df1)
return(df)
} n PI_percentage lower upper cover alpha beta mean_in_interval
1 443 0.95 0.4403352 0.5568129 0.9428698 133 133 TRUE
2 26 0.95 0.4448102 0.5605112 0.9254171 119 119 TRUE
3 407 0.95 0.4078696 0.5932908 0.9496711 55 55 TRUE
4 92 0.95 0.4457683 0.5502979 0.9422730 165 165 TRUE
5 146 0.95 0.4427047 0.5557669 0.9510242 151 151 TRUE
6 496 0.95 0.4465372 0.5518538 0.9528252 177 177 TRUE
7 15 0.95 0.4492564 0.5509363 0.9357580 165 165 TRUE
8 222 0.95 0.3627269 0.6238542 0.9549371 29 29 TRUE
9 105 0.95 0.4534146 0.5534927 0.9513511 197 197 TRUE
10 29 0.95 0.4033115 0.6006820 0.9691219 59 59 TRUE